Nonequivariantly, covering spaces over a connected (locally nice) space $X$ are in one-to-one correspondence with actions of the fundamental group of $X$ on discrete sets. For nonconnected spaces we consider instead actions of the fundamental groupoid. In this paper we generalize to the equivariant case, showing that we can use either of two possible notions of action of the equivariant fundamental groupoid. We consider both equivariant covering spaces and the more general notion of equivariant homotopy covering spaces.
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机译：不变地，覆盖连通的（局部良好的）空间$ X $上的空间与$ X $的基本组在离散集合上的动作一一对应。对于非连通空间，我们考虑使用基群的动作。在本文中，我们推广到等变情况，表明可以使用等变基本基群的两种可能的作用概念之一。我们既考虑了等变覆盖空间，也考虑了等价同伦覆盖空间的更一般的概念。
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